Goodness-of-fit tests for modified multinomial logit models

Abstract

Since the performance of Pearson’s χ 2 and deviance tests typically used to evaluate goodness of fit of multinomial models depends on sample size and number of categories, the resulting p-values may become distorted. Having that fact as a basis, this article explored a modification in the construction of the above cited tests by replacing the estimates of maximum likelihood with the introduction of a posterior mean. The performance of the modified tests was evaluated in comparison with the results of conventional tests obtained by Monte Carlo simulation using original specifications. Due to the conservative results, we concluded that the modification made by the inclusion of prior information Beta(5, 5) in building the deviance test resulted in a promising test with satisfactory power values. The results of the modified Pearson’s χ 2 test showed that, for some evaluated cases, the type I error values were not consistent with the specified nominal level, suggesting that the conventional form of this test is more appropriate to assess multinomial logit models goodness-of-fit.